It looks like you've provided an image containing a mathematical expression, likely related to correlation or regression calculations based on its structure.

Here is a breakdown of the formula:

The given formula:

[ r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}} ]

Where:

• $n$ is the number of data points.
• $\sum xy$ is the sum of the products of corresponding $x$ and $y$ values.
• $\sum x$ and $\sum y$ are the sums of the $x$ and $y$ values respectively.
• $\sum x^2$ is the sum of the squares of the $x$ values.
• $\sum y^2$ is the sum of the squares of the $y$ values.

In the expression, I see some large numbers substituted into the formula:

• $\sum xy = 71,085,000,000$
• $\sum x = 255,000$
• $\sum y = 1,010,000$
• $\sum x^2 = 11,422,500,000$
• $\sum y^2 = 87,484,000,000$

These values are then plugged into the formula for $r$.

Steps to calculate $r$:

1. Compute the numerator: $n\sum xy - \sum x \sum y$.
2. Compute each part of the denominator:
   • $n\sum x^2 - (\sum x)^2$
   • $n\sum y^2 - (\sum y)^2$
3. Take the square root of the product of the two terms from step 2.
4. Finally, divide the result of step 1 by the result of step 3 to get $r$.

Would you like me to perform the full calculation, or provide any further clarification on the formula?

Relative Questions:

1. What does the correlation coefficient $r$ signify in this context?
2. How would this formula change for different data sets?
3. How does changing $n$ (number of data points) affect the value of $r$?
4. Can you explain the significance of squaring the sums in the denominator?
5. How is this formula applied in linear regression analysis?

Tip:

When calculating large sums and squares, it's important to double-check the units and scales of the data to avoid rounding errors in large number computations.